Summary: Spreading according to simple rules (e.g., of fire or diseases) and shortest-path distances are studied on -dimensional systems with a small density per site of long-range connections (‘small-world’ lattices). The volume covered by the spreading quantity on an infinite system is exactly calculated in all dimensions as a function of time . From this, the average shortest-path distance can be calculated as a function of Euclidean distance . It is found that for
and for . The characteristic length , which governs the behavior of shortest-path lengths, diverges logarithmically with for all .